Studies on Estimation of Genetic Variances Under Nonadditive Gene Action

193 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988.The main objectives of this study were: (1) to derive a computationally efficient method for inverting a large additive x additive relationship matrix without using conventional matrix inversion, and (2) to develop and evaluate methods for estimating additive, dominance and additive x additive variances in a population in linkage equilibrium. The theory employed for objective (1) involves an extension of Henderson's rapid method for inverting a numerator relationship matrix, and the approach taken was based on a recursive relationship between additive x additive genetic deviations of offspring and parents. The efficiency of this method depends on the structure of the variance-covariance matrix of segregation residuals in relatives. It was shown that under an animal model with additive x additive effects, sire ranking based on the expected merit of a future offspring depends on the relationship between the sire and his mate. Computer simulation was used to evaluate the methods considered in objective (2): restricted maximum likelihood (REML) for normal data, and an extension thereof for threshold models. Asymptotic theory indicated that in a genetic model with additive, dominance and additive x additive effects, the most difficult parameter to estimate was the variance "due to" epistasis, and that several thousand families are required to obtain reliable estimates of this parameter. Results were based on 20 replicates, each with 500 families of 18 individuals. In most cases, empirical sampling variances of REML estimators of variance components were smaller than asymptotic variances. This indicates that tests of significance for variance components based on asymptotic theory may be conservative. In the presence of additive x additive effects, biases, mean squared errors and empirical variances of additive and dominance variance estimators were larger; further, sampling properties mentioned above of the additive and additive x additive variance estimators were affected by linkage. As expected, with discrete data, the estimates were much more imprecise, in relative terms, than those obtained with normal data. The results suggest that animal breeding experiments of sufficient size carried out with laboratory animals or livestock to estimate non-additive variances may not be feasible in practice. As indicated by the results, estimates of the parameters should include a measure of dispersion because of the large variation expected to be encountered, even when working with "large" data files. More efficient designs and more sensitive methods of variance component estimation are required to obtain satisfactory estimates of non-additive genetic variances.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD